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2 Cash transfer VS inkind transfer Consider a consumer who consumes two goods: good 1 as money spent on all other goods and good 2 as education, with utility function U(x1,x2) : xlxg, and budget constraint x1 + 50x2 : 10000. 2.1 Find the utilitymaximizing quantities of goods 2171 and 3:2 as a function of 5. Suppose the government would like to increase the welfare of this consumer by subsizing education. One proposal is to increase the consumer's income from 10000 to 15000 (for example, by introducing a program like the earned income tax credit). Let's call this policy as cash transfer program. 2.2 State the new budget constraint and calculate the new utilitymaximizing quan tities of goods 3:1 and 3:2. Compare your answers to those of 2.1. Now, consider an alternative program that simply gives the consumer 100 units of good 2 (for example, the Pell grant program that provides grants that can be spent only on education). Let's call this as the mkmd transfer program. You might have noticed that the two programs have the same cost. 2.3 Illustrate the consumer's budget constrant in this case. Note that the constraint is not linear anymore. 2.4 Now, let's consider some cases involving dierent values of E). First, let 5 : 1. Show that the optimal value of $2 under the cash transfer is more than 100. Explain Why, in this case, the consumer is equally welloff under the cash transfer and inkind transfer program. 2.5 Show that the amount of 3:2 consumed under the cash transfer program is in creasing in I). Find a value 39* such that the optimal value of 5152 under the cash transfer program is 100. Explain Why the consumer Whose value of b is above 5* is equally welloff under the cash transfer and inkind transfer program. 2.6 Consider a consumer for whom 33